The foundation has been battling the Port Authority for months over how to pay for the ballooning costs of the underground museum at the World Trade Center site, which will house twisted steel from the Twin Towers, a crushed fire truck and other large artifacts of the attack, along with a repository of unidentified victims' remains.

The Port Authority claimed last year that the museum owed $300 million to cover cost overruns on the project. Bloomberg countered that the Port Authority owed the museum about $140 million because of construction delays.

Work on the project all but stopped amid the funding disagreement, leading officials to say late last year that the museum would not open as scheduled on the 11th anniversary of 9/11 this September.

But both sides have also long said they were confident they would resolve the dispute eventually, and after a closed-door meeting last week, it appeared this week that they were finally close to a deal.

In addition to Bloomberg's optimistic comments, Patrick Foye, the Port Authority's chairman, said at a New York state Senate hearing Tuesday that "a significant number of the issues have been resolved," the Associated Press reported.

And Bloomberg, who spoke at an unrelated press conference in The Bronx, added that the Port Authority has done a "spectacular" job rebuilding the extremely complex World Trade Center site.

"The Port Authority was late delivering some stuff from [the] museum, but that’s the real world," Bloomberg said. "That’s no reason to go yell and scream at everybody…. As long as we’re going in the right direction and doing it together, this memorial museum’s going to get done."

These World Trade Center steel tridents will stand in the entrance to the underground 9/11 museum. View Full Caption

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